Question

if
$x = ( \sqrt{3} + \sqrt{2} ) \div \sqrt{3} - \sqrt{2}$
and
$y =( \sqrt{3} - \sqrt{2} ) \div \sqrt{3} + \sqrt{2}$
find
${x}^{2} + {y}^{2}$
​

Answer 1

Step-by-step explanation:

x=(√3+√2)/(√3-√2)

y=(√3-√2)/(√3+√2)

x+y=(√3+√2)/(√3-√2)+(√3-√2)/(√3+√2)

={(√3+√2)^2+(√3-√2)^2}/(√3+√2)(√3-√2)

=(3+2+2√6+3+2-2√6)/(√3^2-√2^2)

=10/(3-2)

=10/1

=10

x^2+y^2

=(x+y)^2-2xy

=(10)^2-2.(√3+√2)/(√3-√2).(√3-√2)/(√3+√2)

=100-2

=98